\documentclass[border=0.2cm]{standalone}
% Required package
\usepackage{tikz}
\usepackage{zenburn}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    view={20}{20},
    axis lines=center,
    ticks=none,
    xmin=-.1,xmax=1.5,ymin=-.1,ymax=1.1,zmin=-.5,zmax=1.5,
    xlabel={$h_1$},ylabel={$h_2$},zlabel={$h_3$},
    ]

    % plot dots for the two points
    \addplot3 [only marks, draw=zenred, fill=zenred] coordinates {(0.1,0.8,0.9)};
    \addplot3 [only marks, draw=zenblue, fill=zenblue] coordinates
    {(0.8,0.2,0.2)};
    \addplot3 [only marks, draw=zenorange, fill=zenorange] coordinates {(0.3,0.7,1.0)};
    \addplot3 [only marks, draw=zengreen, fill=zengreen] coordinates {(0.6,0.1,0.3)};

    % plot dashed lines to axes
    \addplot3 [no marks,densely dashed, draw=zenred+2] coordinates {(0.0,0.0,0.9) (0,0.8,0.9) (0.1,0.8,0.9)
      (0.1,0,0.9)};
    \addplot3 [no marks,densely dashed, draw=zenred+2] coordinates {(0.1,0.0,0.0) (0.1,0.8,0.0)
      (0.1,0.8,0.9)};
    \addplot3 [no marks,densely dashed, draw=zenred+2] coordinates {(0.0,0.0,0.9)
      (0.1,0.0,0.9) (0.1,0.0,0.0)};
    \addplot3 [no marks,densely dashed, draw=zenred+2] coordinates {(0.1,0.8,0.0)
      (0.0,0.8,0.0) (0.0,0.8,0.9)};

    \addplot3 [no marks,densely dashed, draw=zenblue+3] coordinates {(0.0,0.0,0.2) (0,0.2,0.2) (0.8,0.2,0.2)
      (0.8,0,0.2)};
    \addplot3 [no marks,densely dashed, draw=zenblue+3] coordinates {(0.8,0.0,0.0) (0.8,0.2,0.0)
      (0.8,0.2,0.2)};
    \addplot3 [no marks,densely dashed, draw=zenblue+3] coordinates {(0.0,0.0,0.2)
      (0.8,0.0,0.2) (0.8,0.0,0.0)};
    \addplot3 [no marks,densely dashed, draw=zenblue+3] coordinates {(0.8,0.2,0.0)
      (0.0,0.2,0.0) (0.0,0.2,0.2)};

    % label points
    \node [above] at (axis cs:0.1,0.8,0.9) {猫};
    \node [above right] at (axis cs:0.3,0.7,1.0) {虎};
    \node [above] at (axis cs:0.8,0.2,0.2) {狗};
    \node [above] at (axis cs:0.6,0.1,0.3) {鬣狗};
    \node [below right] at (axis cs:0,0,0) {$O$};
  \end{axis}
\end{tikzpicture}
\end{document}